    Let \({P}_n \)  denote the space of all complex polynomials \(P(z)=\sum _{j=0}^{n}a_{j}{z}^{j}\)  of degree \(n\) .
A famous result known as Bernstein's inequality (for reference, see [1]}, [2]} or [3]} states that if \(P\in {P}_n\) , then
\(\underset{\left|z\right|=1}{Max}\left|P^{\prime }(z)\right|\le n\underset{\left|z\right|=1}{Max}\left|P(z)\right|,\) 
